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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 7: Q13. (page 404)

Simplify the expression
${(4 a^{4} b^{9} c)}^{2}$

Short Answer

Expert verified

The simplified version of ${(4 a^{4} b^{9} c)}^{2}$ is $16 a^{8} b^{18} c^{2}$ .

Step by step solution

01

Step 1. State the product power law of ‘laws of indices’.

According to this law, when a product is raised to a power, every factor of the product is raised to the power.

In general: ${(x y)}^{m} = x^{m} y^{m}$

02

Step 2. State the ‘Law of indices’ for power of index numbers.

If a term with a power is itself raised to a power then the powers are multiplied together.

In general: ${(x^{m})}^{n} = x^{m 脳 n}$

03

Step 3. Simplify the expression.

The given expression is: ${(4 a^{4} b^{9} c)}^{2}$

First apply the product power law to simplify the given expression.

${(4 a^{4} b^{9} c)}^{2} = {(4)}^{2} {(a^{4})}^{2} {(b^{9})}^{2} {(c)}^{2}$

Apply the 鈥楲aw of indices鈥� for power of index numbers and simplify further.

${(4 a^{4} b^{9} c)}^{2} = {(4)}^{2} {(a^{4})}^{2} {(b^{9})}^{2} {(c)}^{2} = 16 (a^{4 脳 2}) (b^{9 脳 2}) (c^{2}) = 16 (a^{8}) (b^{18}) (c^{2}) = 16 a^{8} b^{18} c^{2}$

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Most popular questions from this chapter

MULTIPLE REPRESENTATIONS in this problem, you will explore exponents.

a. TABULAR Copy and use a calculator to complete the table.

b. ANALYTICAL What do you think the values of $5^{0}$ and $5^{鈭� 1}$ are? Verify your conjecture using a calculator.

c. ANALYTICAL Complete: for any nonzero number a and any integer n, $a^{鈭� n} =_.$

d. VERBAL Describe the value of a nonzero number raised to the zero power.

Simplify the expression

$(鈭� 2 g^{3} h) {(鈭� 3 g j^{4})}^{2} {(鈭� g h j)}^{2}$

MULTIPLE CHOICE Antonia is carpeting two of the rooms in her house. The dimensions are shown. What is the total area to be carpeted?

F $x^{2} + 3 x$

G $2 x^{2} + 6 x 鈭� 10$

H $x^{2} + 3 x 鈭� 5$

J $8 x + 12$

Read each question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.

Simplify the following expression.

${(\frac{2 w^{2} z^{5}}{3 y^{4}})}^{3}$

F $\frac{2 w^{5} z^{8}}{3 y^{7}}$

G $\frac{8 w^{6} z^{15}}{27 y^{12}}$

H $\frac{8 w^{5} z^{8}}{27 y^{7}}$

J $\frac{2 w^{6} z^{15}}{3 y^{12}}$

Choose a term from the Key Vocabulary list above that best describes the given expression.

$5^{鈭� 2} = \frac{1}{5^{2}}$

See all solutions

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